An arithmetic sequence is a list of numbers (terms) with a constant difference (d) between each term. You add the same number to get from one term to the next.

Notes

 

Practice Problems

\(\textbf{1)}\) Find the next three terms of the sequence \(3, 7, 11,\ldots\)

Show Answer

The answer is \(15,19,23\)

 

\(\textbf{2)}\) Find the next four terms of the sequence \(45, 38, 31,\ldots\)

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The answer is \(24,17,10,3\)

 

\(\textbf{3)}\) Find the rule of the sequence \(3, 7, 11,\ldots\)

Show Rule

The rule is \(a_n=3+4(n-1) \text{ or } a_n=4n-1\)

 

\(\textbf{4)}\) Find the rule of the sequence \(45, 38, 31,\ldots\)

Show Rule

The rule is \(a_n=45-7(n-1) \text{ or } a_n=-7n+52\)

 

 

Find the missing value

\(\textbf{5)}\) \(a_1=3,\,d=5,\,\) what is \(a_8\)?

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The answer is \(a_8=38\)

 

\(\textbf{6)}\) \(d=-2,\, a_5=10,\,\) what is \(a_1\)?

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The answer is \(a_1=18\)

 

\(\textbf{7)}\) \(a_1=7,\, a_6=22,\,\) what is \(d\)?

Show Answer

The answer is \(d=3\)

 

See Related Pages

\(\bullet\text{ Geometric Sequences}\)
\(\,\,\,\,\,\,\,a_n=a_1 \cdot r^{(n-1)}…\)

\(\bullet\text{ Arithmetic Series}\)
\(\,\,\,\,\,\,\,s_n=\frac{n}{2}(a_1+a_n)…\)

\(\bullet\text{ Geometric Series}\)
\(\,\,\,\,\,\,\,s_n=a_1 \frac{1-r^n}{1-r}…\)

\(\bullet\text{ Infinite Geometric Series}\)
\(\,\,\,\,\,\,\,s_\infty = \frac{a_1}{1-r}\,\,\, |r| \lt 1…\)

\(\bullet\text{ Summation Notation}\)
\(\,\,\,\,\,\,\, \displaystyle \sum_{i=4}^{9} 3i-5 …\)

\(\bullet\text{ Recursive Sequences}\)
\(\,\,\,\,\,\,\, a_{1}=2, \, a_{n+1}=a_{n}+3…\)

\(\bullet\text{ Andymath Homepage}\)